Fenestration Product Such as a Skylight Having a Laminated Glazing Unit

ABSTRACT

A fenestration is provided having a peripheral frame defining a frame opening, the frame being adapted to being installed upon an opening in a building panel. Cooperating with the peripheral frame is a laminated panel which is structurally mounted to and sealingly spans the peripheral frame opening to form a structural and leak proof interconnection. The laminated panel is formed of three structural layers; an outer and inner plastic sheet and a resin layer interposed therebetween which are collectively bonded together to form a structural laminate, the laminated panel being capable of transmitting visible light therethrough.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to fenestration products, particularly, askylight having a laminated glazing unit.

2. Background Art

Fenestration building products have been used to allow light intoresidential, commercial, and industrial buildings and typically fit inan opening in the building. Examples of fenestration products includeskylights and tubular skylights. Skylights typically do not require thesame degree of optical quality of windows. Therefore, low cost andlightweight plastic panels can be used in place of glass. Skylights aretypically formed of a light transparent panel of glass or plasticmounted in a peripheral frame formed of wood, metal or extruded plastic.In order to achieve structural rigidity the plastic panels arefrequently outwardly domed in a convex manner, the peripheral edges ofthe plastic panels being mounted in a rectangular or circular mountedframe.

Skylights are typically mounted on non-vertical surfaces of thebuilding, particularly a roof. As a consequence, they are subjected todamage when items fall on them. Examples of these items may includehail, swaying tree limbs, or wind driven missiles such as during ahurricane. Sudden breaching of the skylight window subjects theunderlying room to potentially substantial water damage and possiblycould pressurize or depressurize the building causing the failure ofother windows or doors. In extreme situations, breaching a skylight canallow strong winds to pressurize a building leading to the loss of aroof or other major structural failures.

In order to address missile impact failures, skylights in hurricaneregions frequently use laminated tempered glass panels or very thickwall domed acrylic panels. However, laminated glass canopies arerelatively heavy and relatively expensive. Their weight often demandsstronger, more expensive support structures, like the door, larger roofjoists, and larger size equipment for installation. Both of theseincrease the overall cost of the skylights.

What is needed is an inexpensive fenestration product which isinexpensive and lighter in weight that prevents catastrophic breachingsuch as with skylights by falling or windblown debris.

SUMMARY OF THE INVENTION

In its simplest form, the present invention comprises a fenestrationproduct, such as a window or a skylight, to be mounted in a buildingopening. The fenestration product is provided with a peripheral frame tobe mounted on the building defining a frame opening. Within the frameopening is a laminated panel capable of transmitting visible light intothe building. The laminated panel is an outer periphery which is held bythe peripheral frame spanning the panel opening. The laminated panel ismade up of a first sheet of plastic, a second sheet of plastic and aninterposed layer of resin which bonds the first and second sheets ofplastic internal resin layer into a structural member. The laminatedpanel is selectively formable into a three-dimensional shape.

A preferred embodiment of the invention is a skylight assembly having aperipheral frame defining a frame opening. Within the frame opening is alaminated panel which sealingly cooperates with the peripheral frame toclose the peripheral frame opening. The laminated panel is transparentto visible light and is made up of three layers, a first sheet ofplastic, an intermediate sheet of resin and a second sheet of plasticwhich are collectively bonded together to form a laminate. Preferably,the laminate is selectively thermal formed so that the central region ofthe laminate forms a dome.

Another preferred embodiment of the invention, the dome laminated panelhas a the peripheral frame molded in situ about to form a leak resistantbond between the single piece molded frame and the laminated panel.

In yet another embodiment of the invention, the skylight assemblydescribed above having a peripheral frame and a laminated panel isfurther provided with the secondary transparent panel located in spacedrelation to the laminated panel and cooperating with the frame to definean enclosed space which is filled with gas to improve the insulatingqualities of the skylight assembly.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a side elevational view of a skylight used as part ofa tubular skylight assembly installed in a building on a roof;

FIG. 2 illustrates a perspective view of a skylight according to anembodiment of the present invention;

FIG. 3 illustrates a fragmentary cross-sectional view taken along line3-3 of FIG. 2 according to an embodiment of the present invention;

FIG. 4 illustrates a perspective view of an alternative rectangularskylight embodiment of the present invention; and

FIG. 5 illustrates a fragmentary cross-sectional view taken along line5-5 of FIG. 4.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

Reference will now be made in detail to compositions, embodiments, andmethods of the present invention known to the inventors, however itshould be understood that the disclosed embodiments are merely exemplaryof the present invention which may be embodied in various alternativeforms. Therefore, specific details disclosed herein are not to beinterpreted as limiting rather merely as a representative basis forteaching one skilled in the are to variously employ the presentinvention. Except where expressly indicated all numerical quantities inthis description indicating the amounts of material or conditions it isunderstood as modified by the word “about” in describing the broadestscope of the present invention. Practice within the numerical limits isgenerally preferred.

In referring to FIG. 1, a building 2 is illustrated with a non-verticalsurface, namely a roof 4. The roof 4 has an opening 6 into which askylight assembly 8 is fitted. The skylight assembly 8 includes askylight canopy 10 connected to a frame 12. The frame 12 is optionallyprovided with a curb 14 and a flashing 15. The skylight assembly 8 has acollector 16 reflective interior surface which is adjacent to a joist 18of the roof 4. The reflective interior surface of collector 16 isconnected to a light pipe 20 which will conduct light to an interiorroom below defined by the ceiling of the room 22. The ceiling of theroom 22 has an opening 24 through which the light pipe 20 passes and isconnected to an interior flange 26 that is adjacent to the interior roomside of the ceiling 22. Attached to the interior flange 26 is a diffuser28 that permits light from the skylight to be spread more broadly aboutthe room below.

It should be understood that the reflective interior surface ofcollector 16, the light pipe 20, the interior flange 26, and thediffuser 28 are optional items in the skylight assembly 8.

The optional curb 14 and flashing 15 may be secured to the roof bymethods known in the art. It should be understood that the frame 12 mayinclude other securing elements without exceeding the spirit of theinvention.

It should be further understood that while illustrations of certainembodiments are directed to skylight assemblies, other fenestrationproducts may not exceed the spirit of the invention. Non-limitingexamples of other fenestration products may include windows, patiodoors, sidelights, doorlites, and transoms.

Referring now to FIG. 2, a circular skylight embodiment 8 is illustratedshowing an example of the current invention. It should be understoodthat the shape of the skylight may be an architectually suitable shapeproviding sufficient structural and sealing integrity, such as round,oval, square, or rectangular shapes. In this example, the skylightdirectly opens into the building interior space without using a lightpipe 20.

Referring to FIG. 3 which is an embodiment of the cross-section 3-3shown in FIG. 2, the canopy 10 is illustrated as having a first sheet ofplastic 40 having a periphery 42, a second sheet of plastic 44 having aperiphery 46, and a resin layer 48 with a periphery 50.

The sheets of plastic 40 and 44 may be formable when laminated with theresin layer 48 in certain embodiments. These sheets range in thicknessfrom 0.75 mm to 100 mm, with typical thicknesses independently selectedfrom 2 mm, 3 mm, 4 mm, 5 mm, 10 mm or 20 mm. Non-limiting examples offorming processes for these sheets may include thermoforming, vacuumforming or pressure forming. The forming process in certain processesmay occur at a temperature below a melting point of the selectedplastics used in sheets 40 and 44. The processing temperature forforming should exceed a service temperature for the skylight, which incertain embodiments may range from 60-95° C. Examples of formablematerials include acrylic and polycarbonate.

The sheets of plastic 40 and 44 are adjacent to the resin layer 48. Itshould be understood that the plastic 40 and 44 may be bonded, adheredor otherwise secured to the resin layer to form a multi-layer structurallaminate. The fitness-for-use requirements of the inner plastic sheet 44may be less stringent than the outer plastic sheet 40. The sheet 40being on the outer layer may be exposed to a harsher environment thanthe sheet 44 on the inner layer in regards to temperature extremes,ultraviolet radiation, physical abrasion, and other conditions. Itshould be understood that the outer and inner sheets may be different oridentical materials without violating the intent of the invention.Examples inner plastic sheets 44 may further include polyolefin, vinyl,and terephthalate. Since the inner plastic sheets 44 may not provide asmuch structural strength as the outer plastic sheets 40 the thickness ofthe inner sheet 44 may also be relatively thinner than the outer plasticsheet 40.

The resin layer 48 may be comprised of a resin. Non-limiting examples ofthe resin include polyvinyl butyral, ethylene vinyl acetate polymer orcopolymer, or polyethylene. The resin layer may be applied as a liquid,a film or a sheet according to certain embodiments of this invention.Other physical forms of the resins may be used in this invention withoutviolating the intent of the invention.

The periphery 51 of the canopy 10 which includes the periphery 42 of thefirst sheet 40, the second sheet 44 and the resin layer 48 is overmoldedinto the peripheral frame 12. It should be understood that other meansof securing the canopy 10 to the frame 12 may be used without violatingthe spirit of this invention. Examples of securing means may include agasket or a sealer. In certain embodiments, an optional spaced apartinner layer of plastic 52 may be included in the skylight assembly 8 inorder to improve the thermal transmission resistance of the assembly 8.The multi-layer canopy 10 and the inner plastic layer 52 are preferablybonded together about their peripheral edges by a two-sided tape seal 53to form an insulated unit. The two-sided tape seal 53 is described indetail in co-pending commonly owned U.S. patent application Ser. No.11/671,657, entitled “Polymeric Insulated Glazing Unit with MoldedFrame”, which is incorporated herein in its entirety.

The frame 12 may be formed of multiple pieces in a conventional manner.The multiple pieces may be fitted around the periphery of the canopy 10to form the skylight assembly 8. An example is a rectangular framehaving four individual frame sections that may corner-keyed and sealed.The frame is then sealed to the laminated panel using methods andmaterials known in the art.

Preferably the frame 12 is formed as a single piece. The single piecemay be made as a separate molded part having no joints. The separatemolded part then being sealed to the laminated panel. As an alternative,the frame 12 may be the single piece molded in-situ encapsulating theperiphery of the laminated panel and simultaneously forming a watertightseal.

Materials that may be suitable for forming a single piece frame mayinclude polymers, such as thermoset plastics like reaction injectionmolded plastics, thermoplastics, and fiber reinforced plastics. Thesematerials may be shaped by processes known in the art, such as reactioninjection molding, high pressure injection molding, extrusion,thermoforming, or compression molding.

Further, the skylight assembly 8 either alone or as part of a tubularskylight may have a reflective interior surface 54. This provides a goodseal against dust and other small debris dropping from the inside of theroof, as well as allowing the skylight to be trim finished from aninterior perspective. The reflective interior surface 54 aids intransmitting light to the room below. In addition, the reflectiveinterior surface 54 may also connect with the light pipe 20 to furtherenhance the amount of light going to the room.

An example of the skylight assembly having the light pipe is disclosedin detail in co-pending, commonly owned U.S. patent application Ser. No.11/671,726, entitled “Overmolded Fenestration Building Product andMethod of Manufacture”, which is incorporated herein in its entirety.

As an option, a mar-resistant coating 56 may be applied to an exteriorexposed surface of the plastic sheet 40 of the canopy 10. Siloxane orpolymethyl methacrylate coatings or the like can be used to provide ahard, mar resistant exterior surface to the canopy 10.

To make the skylight assembly 8, take two sheets of plastic 40 and 44which will be large enough to span the opening 6. In certainembodiments, the first 40 and second 44 sheets are bonded together byinterposing the resin layer 48 between them. The sheets are laminatedusing methods known in the art. Non-limiting examples of methods mayinclude pressure and/or heat, or heat under vacuum. Such a step removesany gas that may be trapped between the layers, as well as provides anycuring or bonding necessary for the resin layer 48.

The laminated panel formed above optionally may be formed into athree-dimensional shape, such as a pyramid, a dome or similar convexconfiguration. The three-dimensional shape may provide additionalstructural strength relative to a flat sheet. Further, thethree-dimensional configuration may less the impact force by deflectingthe impact of some of the energy of relatively concentrated short-termloads such as 2″×4″ lumber missiles driven by a hurricane-force wind.These concentrated short-term loads are simulated by a missile impacttest like TAS 201 used by the Miami-Date County Building Department. Asdescribed above, the laminated sheet may be formed using processes knownfor shaping. In an example of an embodiment of the method, a laminatedpanel may be positioned in a first mold half which is warmedsufficiently to soften the laminated panel. By applying a relativelymild pressure, the laminated panel, when softened, may then be shaped toconform to the first mold half. The laminated panel, once shaped, can beremoved from the first mold half and positioned in a second mold that isa closed mold. The closed mold then is injected with a plastic in anarea adjacent to the periphery of the laminated panel.

In this embodiment of the method of making the skylight assembly 8, acontinuous frame 12 of plastic is molded in situ and the plastic forms aseal between the frame and the laminated panel. Once the frame 12 iscured, a substantially complete skylight assembly 8 can then be removedfrom the open mold. Forming the single piece frame encapsulating thelaminated panel eliminates extra seals and joints, and is an example ofthe method to limit the opportunities for water to leak into a residenceor commercial building. Seals and joints of other designs maydeteriorate with environmental exposure, as well as fail due to fatigueoriginating with cyclic wind pressures and thermal expansions. Theformation of a molded polymer frame is disclosed in published U.S.patent applications US2005/0178078A1 dated Aug. 18, 2005 andUS2005/0055901A1 dated Mar. 17, 2005, both of which are co-pending,commonly owned, and incorporated by reference herein in their entirety.

The leak-tightness of the skylight assembly 8 may be tested according toASTM E547-00 and ASTM E331-00. For areas of the United States that oftensuffer hurricane force winds and driven rain, an acceptance criterionfor these standards is allowing no leakage during the period of thetest. Structurally, the skylight assembly 8 may be tested according toASTM E330-02 where there is a positive and negative wind load placed onthe skylight assembly 8. The acceptance standard for a hurricanevelocity wind zone is where the skylight assembly 8 exceeds the load of250 pounds per square foot.

Even more significant performance criteria for the skylight assembly 8are the missile impact test and a cycling test of TAS201 and TAS203 usedby the Miami-Dade County Building Department. When measured using thesetwo methods, an acceptance criterion is that no cracks or tears occur inthe skylight assembly 8 at less than 90 pounds per square foot of forcewhen measured using TAS203.

FIG. 4 illustrates an alternative embodiment of the invention; arectangular skylight 60. The rectangular skylight 60 includes aperipheral frame 62 which is generally rectangular in shape defining arectangular frame opening 64. Oriented within frame opening 64 is alaminate panel 66 which has a rectangular outer peripheral edge whichcooperates with frame 62 in a secure and water-tight manner. Preferably,laminated panel 66 is convexly domed as shown. Laminated panel 66 istransparent to visible light, and it can either be transparent ortranslucent. Frame 62, as illustrated, is of a simple cap constructionadapted to fit upon a raised curb mounted on the building roof opening.Alternatively, frame 62 can have an integrally formed curb and aflashing as illustrated in the FIG. 3 embodiment.

The skylight 60 of FIG. 4 is shown in cross-sectional side elevation inFIG. 5. In this embodiment, a single laminated panel 66 is provided,however, a spaced apart second panel similar to plastic sheet 52 shownin FIG. 3, can be provided if an insulated skylight is desired. Frame 62is designed to fit over a curb 68 shown in phantom outline in FIG. 5. Asealant is preferably installed between the top surface of the curb andcorresponding cooperating surface of peripheral frame 62. Once installedin place, the screws 70 would be driven through a skirt portion 72 offrame 62 to securely attach the skylight assembly 60 to the curb 68.Preferably, the roofing member 74 will extend between flange 72 and thecurb to provide a water-tight roof system.

EXAMPLE 1

Commercial buildings are using large skylights to allow natural lightinto the building and reduce their reliance on florescent overheadlighting. Such a commercial skylight is a curb-mounted cap. In thisexample, a curb with the outside maximum diameter of 46″×94″ can beprepared in the commercial roof to receive the nominal 4′×8′curb-mounted cap having a laminated panel. The laminated panel iscomprised of two 3 mm thick sheets of polymethyl methacrylate with 1.5mm thick layer of polyvinyl butyral resin between the two sheets ofacrylic. The laminated panel then is thermoformed into the shape of adome. The domed laminated panel is then encapsulated with a frame ofaliphatic polyurethane material which is colored bronze for aestheticpurposes. This curb-mounted cap then is mounted on the roof on theprefabricated curb.

EXAMPLE 2

In this example, the skylight for a residence is mounted on the roofhaving less than a 20° slope. A 3′×3′ residential skylight assembly isfitted into a 30.5″×30.5″ rough opening with a self-flashing curbattached to the roof. A curb-mounted cap having maximum outsidedimensions of 34.5″×24.5″ is attached to the seamless self-flashingcurb. The curb is trimmed out on the interior using approximately ¼″thick sheets of trim stock wood. Trim stock is attached to the roofjoists and finished to meet with the interior ceiling.

The curb-mounted cap includes a laminated panel having a 3 mm acrylicsheet on the exterior layer and a 2.5 mm polyethylene terephthalateinterior layer. Between the layers a sheet of 0.5 mm ethylene vinylacetate copolymer is bonded. The laminated panel is shaped to a domeconfiguration using vacuum-assisted thermoforming at a temperature ofapproximately 120° C. to 150° C.

EXAMPLE 3

For a residence in a high velocity wind zone such as within one mile ofthe Florida coast, a higher impact material may be necessary for thecanopy 10. A skylight having this higher impact resistance is formedwith a laminated panel having 4 mm polycarbonate on the outer layer and2 mm polycarbonate sheet on the interior layer. The polyvinyl butyrallayer in between the two sheets of polycarbonate is 2.5 mm. The outerlayer of polycarbonate is protected with a coating of polymethylmethacrylate for increased resistance to degradation by ultravioletlight. On top of the polymethyl methacrylate layer, a layer oftetraorgano polysiloxane is applied as a scratch resistant coating. Thelaminate is encapsulated in a frame of aliphatic polyurethane material.This forms the curb-mounted cap which is then applied to the residentialseamless self-flashing curb as in Example 2. The cap is secured to thecurb with deck screws or the like.

It should be appreciated that various fenestration products may bemanufactured utilizing the novel laminated panel and frame assembly andthe invention is not limited to skylights per se. While embodiments ofthe invention have been illustrated and described, it is not intendedthat these embodiments illustrate and describe all possible forms of theinvention. Rather, the words used in the specification are words ofdescription rather than limitation, and it is understood that variouschanges may be made without departing from the spirit and scope of theinvention.

1. A skylight assembly, the assembly comprising: a peripheral frame defining an opening; and a laminated panel having a periphery, the panel cooperating with the peripheral frame and spanning the opening, the laminated panel having a first sheet of plastic, a second sheet of plastic, and an interposed layer of resin between the first and second sheets of plastic, the first sheet being bonded to the resin layer, the resin layer being bonded to the second sheet, the laminated panel being selectably formable into a three-dimensional shape.
 2. The skylight assembly of claim 1, wherein the frame is a single piece frame.
 3. The skylight assembly of claim 2, wherein a portion of the laminated panel is overmolded by the frame forming a watertight seal when measured by ASTM E547-00 and ASTM E331-00.
 4. The skylight assembly of claim 2, wherein the single piece frame includes a curb.
 5. The skylight assembly of claim 1, wherein the laminated panel is formed in the shape of an outwardly convex dome.
 6. The skylight assembly of claim 1 wherein the dome comprises a thermoformed laminated panel.
 7. The skylight assembly of claim 1, wherein the layer of resin includes polyvinyl butyral, ethylene vinyl acetate or polyurethane.
 8. The skylight assembly of claim 1, wherein at least one sheet of plastic includes an acrylic, a polycarbonate, a terephthalate, a vinyl, or a polyolefin sheet.
 9. The skylight assembly of claim 8, further including a mar-resistant layer adjacent to the plastic sheet.
 10. The skylight assembly of claim 1, further comprising: a third sheet of plastic, wherein the third sheet of plastic and the second sheet of plastic define a cavity spanning a portion of the opening.
 11. The skylight assembly of claim 1, further having a reflective interior surface positioned below the opening.
 12. The skylight assembly of claim 11, wherein the reflective interior surface has an end adjacent to a roof member.
 13. The skylight assembly of claim 1, further including a light pipe cooperating with the laminated panel, the light pipe extending to an interior room below the roof.
 14. A skylight assembly comprising: a laminated panel having a periphery, the laminated panel including a first sheet of plastic, a second sheet of plastic, and a layer interposed between the first sheet and the second sheet, the laminated panel being shaped into a convex configuration; and a peripheral frame defining an opening, the frame being configured to connect to a roof and defining an opening, wherein the laminated panel spans the opening.
 15. The skylight assembly of claim 14, wherein the peripheral frame is formed of a moldable polymeric material entrapping the periphery of the laminated panel and forming a leak-tight structural joint therewith, where the structural aspect of the joint is measured according to ASTM E330-02 at a positive/negative load exceeding 250 pounds per square foot, the leak-tightness aspect of the joint being measured according to ASTM E547-00 and ASTM E331-00, allowing no leakage.
 16. The skylight assembly of claim 14, the laminated panel passing tests TAS201 and TAS203, wherein no cracks or tears occur at less than 90 pounds per square foot when measured according to TAS203.
 17. The skylight assembly of claim 14, wherein at least one sheet of plastic is comprised of an acrylic, a polycarbonate, a terephthlate, a vinyl, or a polyolefin plastic.
 18. The skylight assembly of claim 14, wherein the first sheet and the second sheet are comprised of different plastics.
 19. The skylight assembly of claim 14, wherein the peripheral frame is formed of a material including at least one of a reaction injection molding material, a thermoplastic material, or a material filled with reinforcing fibers.
 20. A method for making a skylight assembly, comprising: forming a laminated panel having a periphery by providing a first sheet of plastic, providing a second sheet of plastic, bonding the first and second sheets together by interposing a resin layer therebetween; attaching a frame to the periphery of the laminated panel, the frame adapted to receive the periphery of the laminated panel and configured to be connected to a roof.
 21. The method of claim 20, wherein at least one sheet comprises an acrylic, a polycarbonate, a terephthalate, a vinyl, or a polyolefin material.
 22. The method of claim 20, wherein the resin layer includes polyvinyl butyral, ethylene vinyl acetate, or polyurethane.
 23. The method of claim 20, wherein the frame is a single piece frame.
 24. The method of claim 23, wherein attaching the single piece frame includes applying a plastic adjacent to the periphery of the laminated panel.
 25. The method of claim 24, wherein the plastic includes a thermoset material, a thermoplastic material, or a fiber reinforced plastic.
 26. A method for making a skylight assembly, comprising: providing a first sheet of plastic having a first melting point; providing a second sheet of plastic having a second melting point; providing a layer of resin interposed between the first sheet of plastic and the second sheet of plastic; forming a laminated panel including the first sheet of plastic, the second sheet of plastic, and the interposed layer of resin; degassing the laminated panel to remove a gas from between the first sheet of plastic, the second sheet of plastic, and the interposed resin layer; positioning the laminated panel within a first mold half; warming the laminated panel to a temperature less than the lesser of the first or the second melting points; conforming the laminated panel to the first mold half; removing the formed laminated panel from the first mold half; positioning the formed laminated panel in a closed mold; closing the closed mold; injecting a plastic adjacent to the periphery of the formed laminated panel, to form a continuous frame between the frame and the laminated panel; opening the mold; and removing the skylight assembly.
 27. The method of claim 26, wherein at least one sheet of plastic includes an acrylic, a polycarbonate, a terephthalate, a vinyl, or a polyolefin sheet.
 28. The method of claim 26, wherein the resin includes polyvinyl butyral, ethylene vinyl acetate copolymer, or polyurethane.
 29. The method of claim 26, wherein the plastic injected adjacent to the periphery of the laminated panel includes a reaction injection molded plastic, a thermoset, a thermoplastic, or a fiber reinforced plastic.
 30. A fenestration product for installation within a building opening, the fenestration product comprising: a peripheral frame defining a frame opening and the laminated panel cooperating with the peripheral frame and spanning the opening to provide a structural water-tight connection, a panel formed of three structural layers; a first outer plastic layer, a second inner plastic layer and an intermediate resin layer interposed therebetween, laminated together to form a structural member; wherein the peripheral frame is formed of a single piece of polymeric material which is molded in situ about the outer periphery of the laminated panel.
 31. The fenestration product of claim 30, wherein the fenestration product passing tests TAS 201 and TAS 203, wherein no cracks or tears occur at less than 90 lbs. per square when measured according to TAS
 203. 32. The fenestration product of claim 30, wherein the laminated panel includes a three-dimensional shape. 